2025/07/06 by Angel, Mauricio
#53E20 (secondary) #55N33 #57N65 (primary) #58A12 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2507.04512
We present a comprehensive analysis of Bredon's trick, a powerful local-to-global extension principle with broad applications across differential geometry and computational topology. Our main contributions include: (1) novel applications to stratified pseudomanifolds via Verona cohomology with explicit verification of axiomatic conditions; (2) new frameworks for Ricci flow singularity analysis using local curvature concentration; (3) stability theorems for persistent homology in distributed computational settings; and (4) rigorous applications to medical imaging and neural network topology. By systematically developing the theoretical foundations and providing concrete implementations, this work establishes Bredon's trick as a unifying framework for modern local-to-global arguments in geometric analysis and applied topology.